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MathsAges 16-18

Gradient of a line

Calculate the gradient of a straight line segment joining two coordinate points using rise divided by run. Review suitability for your learners before teaching.

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Age band:Ages 13-15Ages 16-18

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Worksheet StudioPractice pack · Ages 16-18

Gradient of a line

Take your time. Show your thinking.

  1. 1. Find the gradient of the line passing through (2, 3) and (6, 31).

    2 · 3 · 6 · 31 · Gradient of a line

  2. 2. Find the gradient of the line passing through (8, 1) and (12, 37).

    8 · 1 · 12 · 37 · Gradient of a line

  3. 3. Find the gradient of the line passing through (3, 10) and (9, 46).

    3 · 10 · 9 · 46 · Gradient of a line

  4. 4. Find the gradient of the line passing through (8, 3) and (9, 6).

    8 · 3 · 9 · 6 · Gradient of a line

  5. 5. Find the gradient of the line passing through (2, 5) and (5, 29).

    2 · 5 · 5 · 29 · Gradient of a line

  6. 6. Find the gradient of the line passing through (2, 6) and (5, 15).

    2 · 6 · 5 · 15 · Gradient of a line

  7. 7. Find the gradient of the line passing through (7, 4) and (8, 9).

    7 · 4 · 8 · 9 · Gradient of a line

  8. 8. Find the gradient of the line passing through (7, 5) and (11, 21).

    7 · 5 · 11 · 21 · Gradient of a line

  9. 9. Find the gradient of the line passing through (7, 7) and (8, 9).

    7 · 7 · 8 · 9 · Gradient of a line

  10. 10. Find the gradient of the line passing through (7, 6) and (10, 18).

    7 · 6 · 10 · 18 · Gradient of a line

  11. 11. Find the gradient of the line passing through (8, 1) and (9, 4).

    8 · 1 · 9 · 4 · Gradient of a line

  12. 12. Find the gradient of the line passing through (8, 10) and (9, 13).

    8 · 10 · 9 · 13 · Gradient of a line
12 questions · Seed 43 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Gradient of a line

Answers and reasoning. Review before teaching.

  1. 1. Find the gradient of the line passing through (2, 3) and (6, 31).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 3) ÷ (6 − 2) = 28 ÷ 4 = 7.

  2. 2. Find the gradient of the line passing through (8, 1) and (12, 37).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (37 − 1) ÷ (12 − 8) = 36 ÷ 4 = 9.

  3. 3. Find the gradient of the line passing through (3, 10) and (9, 46).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (46 − 10) ÷ (9 − 3) = 36 ÷ 6 = 6.

  4. 4. Find the gradient of the line passing through (8, 3) and (9, 6).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (6 − 3) ÷ (9 − 8) = 3 ÷ 1 = 3.

  5. 5. Find the gradient of the line passing through (2, 5) and (5, 29).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 5) ÷ (5 − 2) = 24 ÷ 3 = 8.

  6. 6. Find the gradient of the line passing through (2, 6) and (5, 15).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 6) ÷ (5 − 2) = 9 ÷ 3 = 3.

  7. 7. Find the gradient of the line passing through (7, 4) and (8, 9).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (9 − 4) ÷ (8 − 7) = 5 ÷ 1 = 5.

  8. 8. Find the gradient of the line passing through (7, 5) and (11, 21).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 5) ÷ (11 − 7) = 16 ÷ 4 = 4.

  9. 9. Find the gradient of the line passing through (7, 7) and (8, 9).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (9 − 7) ÷ (8 − 7) = 2 ÷ 1 = 2.

  10. 10. Find the gradient of the line passing through (7, 6) and (10, 18).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (18 − 6) ÷ (10 − 7) = 12 ÷ 3 = 4.

  11. 11. Find the gradient of the line passing through (8, 1) and (9, 4).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (4 − 1) ÷ (9 − 8) = 3 ÷ 1 = 3.

  12. 12. Find the gradient of the line passing through (8, 10) and (9, 13).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 10) ÷ (9 − 8) = 3 ÷ 1 = 3.

12 questions · Seed 43 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Gradient of a line

Take your time. Show your thinking.

  1. 1. Find the gradient of the line passing through (2, 3) and (6, 31).

    2 · 3 · 6 · 31 · Gradient of a line

  2. 2. Find the gradient of the line passing through (8, 1) and (12, 37).

    8 · 1 · 12 · 37 · Gradient of a line

  3. 3. Find the gradient of the line passing through (3, 10) and (9, 46).

    3 · 10 · 9 · 46 · Gradient of a line

  4. 4. Find the gradient of the line passing through (8, 3) and (9, 6).

    8 · 3 · 9 · 6 · Gradient of a line

  5. 5. Find the gradient of the line passing through (2, 5) and (5, 29).

    2 · 5 · 5 · 29 · Gradient of a line

  6. 6. Find the gradient of the line passing through (2, 6) and (5, 15).

    2 · 6 · 5 · 15 · Gradient of a line

  7. 7. Find the gradient of the line passing through (7, 4) and (8, 9).

    7 · 4 · 8 · 9 · Gradient of a line

  8. 8. Find the gradient of the line passing through (7, 5) and (11, 21).

    7 · 5 · 11 · 21 · Gradient of a line

  9. 9. Find the gradient of the line passing through (7, 7) and (8, 9).

    7 · 7 · 8 · 9 · Gradient of a line

  10. 10. Find the gradient of the line passing through (7, 6) and (10, 18).

    7 · 6 · 10 · 18 · Gradient of a line

  11. 11. Find the gradient of the line passing through (8, 1) and (9, 4).

    8 · 1 · 9 · 4 · Gradient of a line

  12. 12. Find the gradient of the line passing through (8, 10) and (9, 13).

    8 · 10 · 9 · 13 · Gradient of a line
12 questions · Seed 43 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Gradient of a line

Answers and reasoning. Review before teaching.

  1. 1. Find the gradient of the line passing through (2, 3) and (6, 31).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 3) ÷ (6 − 2) = 28 ÷ 4 = 7.

  2. 2. Find the gradient of the line passing through (8, 1) and (12, 37).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (37 − 1) ÷ (12 − 8) = 36 ÷ 4 = 9.

  3. 3. Find the gradient of the line passing through (3, 10) and (9, 46).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (46 − 10) ÷ (9 − 3) = 36 ÷ 6 = 6.

  4. 4. Find the gradient of the line passing through (8, 3) and (9, 6).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (6 − 3) ÷ (9 − 8) = 3 ÷ 1 = 3.

  5. 5. Find the gradient of the line passing through (2, 5) and (5, 29).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 5) ÷ (5 − 2) = 24 ÷ 3 = 8.

  6. 6. Find the gradient of the line passing through (2, 6) and (5, 15).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 6) ÷ (5 − 2) = 9 ÷ 3 = 3.

  7. 7. Find the gradient of the line passing through (7, 4) and (8, 9).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (9 − 4) ÷ (8 − 7) = 5 ÷ 1 = 5.

  8. 8. Find the gradient of the line passing through (7, 5) and (11, 21).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 5) ÷ (11 − 7) = 16 ÷ 4 = 4.

  9. 9. Find the gradient of the line passing through (7, 7) and (8, 9).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (9 − 7) ÷ (8 − 7) = 2 ÷ 1 = 2.

  10. 10. Find the gradient of the line passing through (7, 6) and (10, 18).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (18 − 6) ÷ (10 − 7) = 12 ÷ 3 = 4.

  11. 11. Find the gradient of the line passing through (8, 1) and (9, 4).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (4 − 1) ÷ (9 − 8) = 3 ÷ 1 = 3.

  12. 12. Find the gradient of the line passing through (8, 10) and (9, 13).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 10) ÷ (9 − 8) = 3 ÷ 1 = 3.

12 questions · Seed 43 · Age guidance, not curriculum certification